Frequency-resolved optical gating using cascaded second-order nonlinearities

We demonstrate frequency-resolved optical gating (FROG) using cascaded second-order nonlinearities (up-conversion followed by down-conversion). We describe two different cascaded second-order beam geometries-self-diffraction and polarization-gate-which are identical to their third-order nonlinear-optical cousins, except that they use second-harmonic-generation crystals instead of (weaker) third-order materials. Like the corresponding third-order processes, these new versions of FROG yield the same intuitive traces, uniquely determine the pulse intensity and phase (without direction-of-time ambiguity), and yield signal light at the input-pulse wavelength (which simplifies the required spectral measurements). Most importantly, however, we show that these techniques are significantly more sensitive than the corresponding third-order FROG methods, conveniently allowing, for the first time, the unambiguous measurement of ultrashort ~1-nJ pulses, that is, unamplified Ti:sapphire oscillator pulses